**OUTLINES OF TESTS Paper B**

Statistics (Elective) OUTLINES OF TESTS Paper-A 75 marks Paper-B 75 marks Paper-C (Practical) 50 marks Total 200 marks Syllabi and Courses of Reading Paper- A Candidates are required to attempt at least two questions from each Section. Section- I. Descriptive Statistics: (Weight 2/10) Descriptive and inferential Statistics. Population and samples.

* **Candidates are required to attempt at least two questions from each section.*

__Section -I__

__ __** Sampling and Sampling Distributions:** (Weight 2/10)

Basic concepts. Advantages of Sampling. Probability and non-probability sampling, Sampling and non-sampling errors. Sampling designs of simple random. Stratified, systematic, and cluster sampling. Judgement and quota sampling. Random numbers and their use in sampling calculation of sample mean, proportion and variance of simple random samples and stratified random samples. Sampling distribution of a statistic and its standard error. Distributions of sample mean and difference between two sample means with their properties. Distributions of sample proportion and difference between two sample proportions with properties. Central limit theorem with illustrations. Sampling distribution of sample variance and distribution of ratio of two sample variances. Concept of t,

**c**

**– and F- distributions.**

^{2}**(Weight 2/10)**

__Statistical Inference:__Concept of statistical inference. Estimates and estimators. Point estimation by the methods of moments and maximum likelihood. Properties of point estimators; unbiasedness. Consistency and efficiency. Interval estimation.

Null and alternative hypothesis, simple and composite hypothesis. Two types of errors. Level of significance, p-value and power of the test. Acceptance and rejection regions, one-sided and two-sided tests. Testing of hypothesis for mean, difference between two means, proportion and difference between two proportions; based on large samples. Interval estimation. Confidence interval and its interpretation. Interval estimation of the mean, difference between two means, the proportions and the difference between two proportions of populations with known and unknown variances; based on large samples. Determination of sample size. Testing of hypothesis (based on small samples and unknown population variance) for the mean, difference between two means for paired and unpaired observations. Testing of hypothesis of single population variance (Large sample) and equality of two variances (Large and small samples)

__Statistical inference concerning__

__c__

^{2_}**(Weight 1/10)**

__Distribution:__Testing of hypothesis about the variance. Testing of hypothesis about the equality of more than two variances. Pearson’s test for goodness of fit. Contingency tables and tests for independence and homogeneity. Co- efficient of mean square contingency and its maximum value. Yates correction for continuity. Chi-Square test for the Multinomial probabilities.

#### Section -II

** Analysis of Variance:** (Weight:

*Please see Note No. 2 below*)

Definition, importance and assumptions of Analysis of Variance. Partitioning of sum of squares and degrees of freedom in one-way classification. Testing the equality of means for one-way classification. Partitioning of sum of squares and degrees of freedom in two-way classification. Testing the equality of means for two-way classification. Multiple comparison tests: Least significant difference test, Duncan’s and Newman- Keuls Multiple range test.

** Basic Experimental Designs:** (Weight:

*Please see Note No. 2 below*)

Basic principle of experimental design. Completely randomised, complete block and Latin square designs. Description, layout, statistical analysis, advantages and disadvantages of these designs. Relative efficiency of three basic designs. Applications of these designs.

__(Note No. 2__** ***For Analysis of variance and Basic Experimental Designs common weight is 2/10)*

** Regression and Correlation Analysis:** (Weight 1/10)

Logic of regression and correlation. Scatter diagram. Regression models. Simple linear regression, least square estimates and their properties. Properties of Least Square regression line, standard error of estimate, co-efficient of determination. Multiple linear regression with two regressors, co-efficient of multiple determination Partial and multiple correlation up to three variables. Linear correlation. Correlation co-efficient and its properties. Correlation of bivariate frequency distribution. Partial and multiple correlation for three variables. Rank correlation, Tied ranks. Testing of hypothesis about regression and simple correlation partial and multiple correlation. Interval estimates and tests of hypothesis about regression paramenters, mean prediction and individual prediction. Interval estimation of regression parameters.

**(Weight 1/10)**

__Non-Parametric Tests:__Sign test, Run test. Mann-Whitney U-test, Wilcoxon Signed rank test, Wilcoxon rank sum test.

**(Weight 1/10)**

__Vital Statistics:__Definition of vital events and vital statistic. Uses and shortcomings of vital statistics. Sources of demographic data. Vital rates and ratios: Sex and child woman ratio. Vital Index, Crude, specific and standardized death rates. Crude, specific and standardized birth rates, general and specific fertility rate. Reproduction rates: Gross and Net reproduction rates. Census, registration system of deaths and births in Pakistan.

__Paper- C (Practical)__

*Candidates are required to attempt one question from each section.*#### Section-I

One question from each section of __Paper A__ should be set.

#### Section-II

One question from each section of __Paper B__ should be set.

Each question of 18 marks: .i.e. 18-18 | 36 marks |

Practical Note Book | 05 marks |

Viva Voce: | 09 marks |

Total: | 50 marks |

__Books Recommended:__

- Beg,M.A. and Mirza, M.D.(1997). Statistics, Theory and Methods. Vol.I&II. Carvan Book House, Kachehry Road, Lahore.
- Chaudhrey, S.M. and Kamal, S.(2002). Introduction to Statistical Theory Part-I &II. Illmi Kitab Khana Urdu Bazar, Lahore.
- Chaudhry, R.M.(1998) Polymer Modern Statistics, Polymer’s Urdu Bazar, Lahore.
- Freedman, D; Pisani, R;Parues, R and Adhikari, A (1997). Statistics 3
^{rd}Norton, New York. - Freund, J.E(1990).Modern Elementary Statistics. Prentice Hall, Inc.New Jersy.
- Graybill,I and Burdick (1998).Applied Statistics: A first course in inference. Prentice Hall, New Jersy.
- Haq, Masood-ul (1983) Foundation of Probability and Statistics, Tahir Sons, Urdu Bazar, Karachi.
- Lipschutz, S and Schiller,J (1998). Introduction to Probability and McGraw Hill, New York.
- Polland, A.H; Yousaf, F and Pollard, G,N (1981). Demographic Techniques. Second Edition. Pergaman Press, Oxford.
- Speigal, M.R and Stephens, L.J (1999). Statistics 3
^{rd}McGraw Hill, New York. - Speigal, M.R; Schiller, J.L; Srinivban, R.L (2000). Probability and Statistics 2
^{nd}Schaums out line Series. McGraw Hill, New York. - Walpole, R.E (2001 R). Introduction to Statistics. Macmillan publishing Company.New York/London.
- Wonnacott, T.H. and Wonnacott, R.J (1990). Introductory Statistics. John Wily & Sons. New York.